On the asymptotic formula of L'(1, χ)

Abstract

Let $\chi$ be a quadratic Dirichlet character. In some literatures, various asymptotic formulae of $L^{\prime }(1,\chi )$, under the assumption that $L(1,\chi )$ takes a small value, were derived. In this paper, we will give a new treatment unified for the odd and even cases, not depending on Kronecker limit formula. For imaginary quadratic fields, our result coincides with Proposition 22.10 in [1].

arXiv comment13 pages